I know there are several books which compare Ancient Greek with modern like Jannaris' Historical Grammar. But for modern Greek (including demotic) there is Greek: A Comprehensive Grammar of the Modern Language (Comprehensive Grammars) by David Holton and Vassilios Spyropoulos (Paperback - Mar 15, 2012) http://www.amazon.com/Greek-Comprehensi ... 532&sr=8-3. It's a very thorough modern grammar.

But I just picked up Essential Modern Greek Grammar (Dover Language Guides Essential Grammar) by Douglas Q. Adams (Paperback - Sep 1, 1987) http://www.amazon.com/Essential-Modern- ... 623&sr=8-1. Essential Modern Greek Grammar is just what is needed for a student of Koine to get a quick look at modern Greek. The languages look very similar, once you know that a lot of beginning vowels have fallen away. This book is 90 pages long. Super cheap, and should be read by those who want to have a grasp of the difference between modern Greek and Koine.

You can get the 2nd edition of Greek: A Comprehensive Grammar of the Modern Language on Kindle at Amazon: http://www.amazon.com/Greek-Comprehensi ... ve+grammar. This book has even been translated from English into modern Greek. If you read the introduction online (you can preview the 1st chapter in Kindle format online, along with the introduction), you will get a list of the other grammars of Modern Greek.